This article is cited in 11 papers

Deformations of non-compact complex curves and envelopes of meromorphy of spheres

S. M. Ivashkovich^a, V. V. Shevchishin<sup>b

a</sup> University of Sciences and Technologies
^b Ruhr-Universität Bochum

Abstract: The paper discusses the properties of the envelopes of meromorphy of neighbourhoods of symplectically immersed two-spheres in complex Kahler surfaces. The method used to study the envelopes of meromorphy is based on Gromov's theory of pseudoholomorphic curves. The exposition includes a construction of a complete family of holomorphic deformations of a non-compact complex curve in a complex manifold parametrized by a finite-codimensional analytic subset of a Banach ball. The existence of this family is used to prove a generalization of Levi's continuity principle, which is applied to describe envelopes of meromorphy.

UDC: 517.55+515.17

MSC: Primary 32D10, 58F05; Secondary 32A20, 53C15

Received: 23.01.1998

DOI: 10.4213/sm349

 English version: Sbornik: Mathematics, 1998, 189:9, 1295–1333

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